On quantum and parallel transport in a Hilbert bundle over spacetime

We study the Hilbert bundle description of stochastic quantum mechanics in curved spacetime developed by Prugove\v{c}ki, which gives a powerful new framework for exploring the quantum mechanical propagation of states in curved spacetime. We concentrate on the quantum transport law in the bundle, specifically on the information which can be obtained from the flat space limit. We give a detailed proof that quantum transport coincides with parallel transport in the bundle in this limit, confirming statements of Prugove\v{c}ki. We furthermore show that the quantum-geometric propagator in curved spacetime proposed by Prugove\v{c}ki, yielding a Feynman path integral-like formula involving integrations over intermediate phase space variables, is Poincar\'e gauge covariant (i.e.$\!$ is gauge invariant except for transformations at the endpoints of the path) provided the integration measure is interpreted as a ``contact point measure'' in the soldered stochastic phase space bundle raised over curved spacetime.Comment: 25 pages, Plain TeX, harvmac/lanlma

Conventional Superconductivity in Fe-Based Pnictides: the Relevance of Intra-Band Electron-Boson Scattering

Various recent experimental data and especially the large Fe-isotope effect point against unconventional pairings, since the large intra-band impurity scattering is strongly pair-breaking for them. The strength of the inter-band impurity scattering in some single crystals may be strong and probably beyond the Born scattering limit. In that case the proposed s(+-) pairing (hole(h)- and electron(el)-gaps are of opposite signs) is suppressed but possibly not completely destroyed. The data imply that the intra-band pairing in the h- and in the el-band, which are inevitably due to some nonmagnetic el-boson interaction (EBI), must be taken into account. EBI is either due to phonons (EPI) or possibly due to excitons (EEI), or both are simultaneously operative. We discuss their interplay briefly. The large Fe-isotope effect favors the EPI and the s(+) pairing (the h- and el-gaps are in-phase).Comment: 7 pages, no figures, explanations and argumentations improved, references adde

Thermodynamics of the one-dimensional frustrated Heisenberg ferromagnet with arbitrary spin

The thermodynamic quantities (spin-spin correlation functions <{\bf S}_0{\bf S}_n>, correlation length {\xi}, spin susceptibility {\chi}, and specific heat C_V) of the frustrated one-dimensional J1-J2 Heisenberg ferromagnet with arbitrary spin quantum number S below the quantum critical point, i.e. for J2< |J1|/4, are calculated using a rotation-invariant Green-function formalism and full diagonalization as well as a finite-temperature Lanczos technique for finite chains of up to N=18 sites. The low-temperature behavior of the susceptibility {\chi} and the correlation length {\xi} is well described by \chi = (2/3)S^4 (|J1|-4J2) T^{-2} + A S^{5/2} (|J1|-4J2)^{1/2} T^{-3/2} and \xi = S^2 (|J1|-4J2) T^{-1} + B S^{1/2} (|J1|-4J2)^{1/2} T^{-1/2} with A \approx 1.1 ... 1.2 and B \approx 0.84 ... 0.89. The vanishing of the factors in front of the temperature at J2=|J1|/4 indicates a change of the critical behavior of {\chi} and {\xi} at T \to 0. The specific heat may exhibit an additional frustration-induced low-temperature maximum when approaching the quantum critical point. This maximum appears for S=1/2 and S=1, but was not found for S>1.Comment: 8 pages, 7 figure

On the electronic structure of CaCuO2 and SrCuO2

Recent electronic structure calculations for the prototypical lowdimensional cuprate compounds CaCuO2 ans SrCuO2 performed by Wu et. al. (J. Phys.: Condens. Matter v. 11 p.4637 (1999))are critically reconsidered, applying high precision full-potential bandstructure methods. It is shown that the bandstructure calculations presented by the authors contain several important inconsistencies, which make their main conclusions highly questionable.Comment: 4 pages, 3 figures, submitted to J. Phys. Condens. Matte

Measurement of the vortex-core radius by scanning tunneling microscopy

Using a scanning tunneling microscope operated in a spectroscopic mode we imaged flux-line lattices in niobium diselenide at various external magnetic fields. From the evaluation of a large number of tunneling-current profiles taken across the individual vortices we deduced the dependence of the vortex-code radius on the applied magnetic field. It was found that the core radius shows a pronounced decrease with increasing field, even for H/Hc2<<1. This behavior is qualitatively well characterized by self-consistent solutions of the Usadel equations

New insight into the physics of iron pnictides from optical and penetration depth data

We report theoretical values for the unscreened plasma frequencies Omega_p of several Fe pnictides obtained from DFT based calculations within the LDA and compare them with experimental plasma frequencies obtained from reflectivity data. The sizable renormalization observed for all considered compounds points to the presence of many-body effects beyond the LDA. From the large empirical background dielectric constant of about 12-15, we estimate a large arsenic polarizability of about 9.5 +- 1.2 Angstroem^3 where the details depend on the polarizabilities of the remaining ions taken from the literature. This large polarizability can significantly reduce the value of the Coulomb repulsion U_d about 4 eV on iron known from iron oxides to a level of 2 eV or below. In general, this result points to rather strong polaronic effects as suggested by G.A. Sawatzky et al., in Refs. arXiv:0808.1390 and arXiv:0811.0214 (Berciu et al.). Possible consequences for the conditions of a formation of bipolarons are discussed, too. From the extrapolated muon spin rotation penetration depth data at T= 0 and the experimental Omega_p we estimate the total coupling constant lambda_tot for the el-boson interaction within the Eliashberg-theory adopting a single band approximation. For LaFeAsO_0.9F_0.1 a weak to intermediately strong coupling regime and a quasi-clean limit behaviour are found. For a pronounced multiband case we obtain a constraint for various intraband coupling constants which in principle allows for a sizable strong coupling in bands with either slow electrons or holes.Comment: 34 pages, 10 figures, submitted to New Journal of Physics (30.01.2009

Electronic structure and magnetic properties of Li_2ZrCuO_4 - a spin 1/2 Heisenberg system in vicinity to a quantum critical point

Based on density functional calculations, we present a detailed theoretical study of the electronic structure and the magnetic properties of the quasi-one dimensional chain cuprate Li_2ZrCuO_4 (Li_2CuZrO_4). For the relevant ratio of the next-nearest neighbor exchange J_2 to the nearest neighbor exchange J_1 we find alpha = -J_2/J_1 = 0.22\pm0.02 which is very close to the critical point at 1/4. Owing this vicinity to a ferromagnetic-helical critical point, we study in detail the influence of structural peculiarities such as the reported Li disorder and the non-planar chain geometry on the magnetic interactions combining the results of LDA based tight-binding models with LDA+U derived exchange parameters. Our investigation is complemented by an exact diagonalization study of a multi-band Hubbard model for finite clusters predicting a strong temperature dependence of the optical conductivity for Li_2ZrCuO_4

A decision model for the efficient management of a conservation fund over time

An important task of conservation biology is to assist policy makers in the design of ecologically effective conservation strategies and instruments. Various decision rules and guidelines originate, e.g., from the Theory of Island Biography (MacArthur & Wilson, 1967) and metapopulation theory (Hanski, 1999). Designing effective strategies and instruments, however, is only part of the solution to problems of biodiversity conservation. In the real world, financial resources are scarce, and it is not only important that policies are ecologically effective but also that they are economically efficient, i.e. lead to maximum ecological benefit for a given resource input. Efficiency has been analysed, e.g. in the context of the spatial allocation of conservation funds (Wu & Bogess, 1999) and of the spatial design of compensation payments for biodiversity enhancing land–use measures (Wätzold & Drechsler, 2002). Decision analysis is a helpful tool for integrating knowledge from different disciplines and identifying optimal strategies and policies (e.g., Drechsler & Burgman, 2003). Methods of decision analysis, such as optimisation procedures, are often a core component of ecological–economic models that bring together ecological and economic knowledge via formal models (e.g., Ando et al., 1998, Drechsler & Wätzold, 2001, Johst et al., 2002). Such models do not only allow a static integration of economic and ecological aspects but also to describe the dynamics of ecological and economic systems in an integrated manner (Perrings, 2002). Examples of such dynamic modelling approaches are Richards et al. (1999), Costello & Polasky (2003) and Shogren et al. (2003). In the present paper we investigate a dynamic conservation management problem different from those of the above mentioned authors and tackle the problem of long–term conservation when future financial budgets are uncertain. The background for this problem is that many species can only survive if certain types of biodiversity–enhancing land–use measures are carried out on a regular basis, such as regularly mowing meadows to create habitat for butterflies (Settele & Henle, 2002). This means that funds have to be regularly available over time, because a temporal gap in the availability of funds may irrevocably drive a species to extinction. While over the last two decades or so a growing commitment of society and governments to conserve biodiversity could be observed, that in many cases also included the increasing provision of funds for this purpose, there are signs that this commitment is currently weakening. An example of such signs are opinion polls in some countries (e.g. Germany) showing that environmental and resource protection issues are given a lower priority by the general public than ten years ago. This implies that there is an increasing risk that conservation funds will be lower in the future than today either through a decrease in political support for such funds or through a decline in donations for private organisations that finance conservation funds. This risk forces governments and conservation organisations concerned by the long–term prevention of species loss to explore options which ensure that their policy aims will be achieved even if future funds are lower than today’s. Obviously, one important option is to save part of the current financial resources to counterbalance possible future budget cuts. In this context, the problem arises which proportion of the available budget should be spent now and which proportion later. In summary, there is the problem of efficiently allocating a conservation budget over time to maximise the survival probability of an endangered species, where the current budget is reasonably high and future conservation budgets are expected to decline in the medium term (although the size of these budgets is not known with any certainty). The aim of this paper is to address this problem on a conceptual level. To have a mechanism that is able to transfer current money to the future regardless of subsequent governments’ preferences and policies, we make the assumption that a conservation fund is being established that is independent of any future government’s decisions and administered by an independent agency with the time–consistent objective function to allocate financial resources over time such that the survival probability of an endangered species is maximised. The probability t of a population surviving T+1 periods, each of length t can be written as the product of the probabilities of surviving each individual period (the complete description of the model including a more in–depth discussion of the results than presented here can be found in Drechsler & Wätzold, 2003): where a is some species specific parameter and K(0) is the habitat capacity when no conservation measures are carried out (Lande, 1993; Grimm & Wissel, 2004). Conservation measures increase K(0) by t which costs an amount of money pt = bt with b constant. Parameter depends on the species and is inversely proportional to the coefficient of variation of the population growth rate (Lande, 1993; Grimm & Wissel, 2004). Each year an amount of money gt = ht + t is granted to the conservation manager where ht is the deterministic component and t c [–, +] is random and uniformly distributed to describe uncertainty in the future budgets. Money that is not spent can be moved into a fund Ft from which money can be drawn in later periods. The fund thus develops like Borrowing is excluded, such that in each period only up to an amount Ft + gt can be spent t = 0,...,T (3) In each period the conservation manager has to decide how much money (pt) to spend for conservation in the present period and how much to allocate into the fund F and save for future periods. This inter–temporal optimisation problem is solved via stochastic dynamic programming (e.g., Clark, 1990). Due to the constraint(3) the solution is not straightforward. In each period, two possible solutions may formally occur: a corner solution where all available money is spent (pt = Ft + gt) and an interior solution where less then that is spent and some money is transferred to the next period. It turns out that the optimal payment in a certain period t depends on the number l of consecutive periods following the present period that have an interior solution: One can see that the optimal payment increases with increasing fund Ft but decreases with increasing uncertainty in the grants. The latter has been shown by Leland (1968) in a 2–period model without constraint (3), denoted as “precautionary” saving and explained from the particular shape of the objective function. From eq. (4) one can also see that more money is saved when is large, i.e., when the aim is to conserve species with weakly fluctuating population growth. One can further show that it is optimal to allocate the payments as even over time as far as the constraint (3) allows. If, e.g., we have constantly decreasing grants it is optimal to save in the beginning and spend the saved money in the final periods. The problem now is that the number l depends on the future grants and if these are not known l is not known and can only be approximated by a probability distribution P(l). For the case where a negative trend is expected in the grants, such that gt = h0 – t + t we have determined P(l) and the expected optimal payment. It turned out that if the uncertainty in the grants is large or small compared to their deterministic trend one obtains a solution that is structurally similar to eq. (4), i.e. we have a situation of precautionary saving. In contrast, if the uncertainty was about of the order of magnitude of the trend we found cases where uncertainty increased the optimal payments. The reason is that the uncertainty has two contrary effects. The one is the standard "precautionary saving" effect caused by the shape of the benefit function. The other, opposing effect is that uncertainty may reduce the (expected) number l and thus increase the optimal payment. Sometimes the latter effect is stronger. However, we found strong evidence that the magnitude of such "precautionary spending" is negligibly small and for practical purposes we conclude that uncertainty generally reduces the optimal payment and more money should be saved